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2019 Summer Program for Undergraduate Research (SPUR)

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Information on the Summer 2019 Undergraduate Research Programs 

These are 8 week programs and both will run from June 3, 2019 - July 26, 2019

Summer Program for Undergraduate Research - SPUR
Research Experience for Undergraduates - REU


These summer programs provide the opportunity for undergraduate students of mathematics to participate in leading-edge research.  This year, some projects are designated "SPUR" and others are designated "REU."  The difference between SPUR and REU projects is the funding available:

Student funding for SPUR projects comes from Cornell.  To receive funding you need to be a Cornell student, but do not need to be a US citizen or resident.  Non-Cornell students are welcome to apply, but there is no funding available.  If you are a non-Cornell student and are accepted to the program you will need to provide your own funding.

Student funding for REU projects comes from the US National Science Foundation.  For this, you need to be a US citizen or permanent resident, but do not need to be a Cornell student.  Both Cornell and non-Cornell students are welcome to apply.

If you come with your own funding you will still be subject to the same competitive selection process.

If you are a student (US or International) currently attending and enrolled at a US institution in a full-time 4-year undergraduate program you will be registered through Cornell Summer Session.  The next paragraph describing the International PIRIP Program does not apply to international students who are currently full-time students enrolled in a 4 year undergraduate program at a US institution.

International students (PIRIP Program):  We welcome international students to apply! The PIRIP Program only applies to international students coming directly from overseas/international institutions (or who are international students currently at a US institution in an exchange or internship program). Students accepted to the REU or SPUR programs will be self-funded and will be registered through Summer Session under the umbrella of the Provost’s International Research Internship Program (PIRIP).  For more information on the PIRIP program go to https://global.cornell.edu/provosts-international-research-internship-program and https://global.cornell.edu/sites/default/files/PIRIP_Procedures_070717.pdf.  You will be responsible for paying an administrative fee ($2,190), which is 25% of the current summer extramural tuition rate for 6 credits (S/U Grade – satisfactory/unsatisfactory).  Summer 2019 fee = $1,460 per credit x 25% x 6 credits = $2,190.  You will also be required to carry adequate health insurance that is in compliance with health insurance requirements.  If you do not have a current plan you can purchase one on your own, which Cornell will review and approve for compliance.  Cornell also offers a Student Health Insurance Plan (SHIP) that you can purchase, which is already in compliance.

To apply you will need the following:

  1. Statement about your background, educational goals, and your scientific interests.  Include whatever further information you consider relevant and be sure to include information about your computer experience.
  2. At least two letters of recommendation, which can be uploaded to the application portal.  The reference writer is notified to upload their letter once you enter their information on the application.
  3. Transcripts (unofficial transcripts are accepted), which can be uploaded to the application portal.

To apply go to Cornell 2019 REU/SPUR Application.  The deadline to submit your application will be February 26, 2019, and offers will be made on approximately March 1, 2019.

If you have comments, questions, or concerns please send e-mail to the SPUR and REU coordinators at mathreu@cornell.edu.

SPUR Program Projects

Project 1:  Analysis on Fractals

Directed by Robert Strichartz, rss24@cornell.edu

Students in this project will study properties of functions defined on fractals. For certain fractals, including the Sierpinski gasket, the Sierpinski carpet, and some of the classical Julia sets, there is now a theory of “differential equations.” (See my book, Differential Equations on Fractals, a tutorial, Princeton University Press, 2006.) One of the goals of this project is to obtain more information about solutions of these fractal differential equations, following up on work that has been done by past REU students. Most of the work on this project will involve both computer experimentation and theoretical study, but individual students may put more emphasis on one or the other. We expect that students will be involved in all stages of the process: planning what examples to study, doing the programming for the computations, and interpreting the results (and attempting to prove the conjectures that come out of the process).

Project 2:  Computations in derived algebraic geometry and equivariant cohomology

Directed by Harrison Chen, chenhi@cornell.edu

This project will focus on doing calculations in the emerging field of derived algebraic geometry.  We will focus on studying differential graded algebras and their global avatar, differential graded schemes.  An example of such a calculation is to compute derived intersections, which capture possible non-transversality and which have been studied in the case of smooth subvarieties of smooth varieties; another is to find explicit presentations of derived moduli stacks of local systems on some explicit topological surfaces.  We will investigate possible generalizations of these results to mildly singular varieties in both local and global settings.  Another question involves studying circle-equivariant cohomology with rational coefficients and its relationship with differential graded algebras over a certain differential graded ring.

Students participating in this project should have some exposure to commutative rings or algebraic topology.  Programming experience may be helpful since investigations can be done using software such as Macaulay2.

REU Program Project

Project 3:  Mechanics, Control, Robotics, and Dynamics

Directed by Andy Borum, adb328@cornell.edu

This project will focus on the analysis of problems in mechanics, control theory, and robotics from the perspective of dynamical systems theory. Within mechanics, we will focus on the equilibrium and stability properties of thin elastic structures, and we will use these results to model the behavior of toys such as a Slinky.  Within control theory, we will study problems in optimal control, inverse optimal control, and ensemble control. Within the field of robotics, we will focus on the problem of automated manipulation for deformable objects and on the problem of simultaneously controlling many robots with a limited number of signals.  Finally, within dynamical systems theory, we will study the connections between stability and optimality and how optimality can be used to model collective motion.

Students participating in this project should have strong backgrounds in linear algebra and ordinary differential equations.  Previous experience with computer programming, optimization, classical mechanics, or control theory will be helpful, but is not required. The problems we will solve can be tailored to students' expertise, and the problems can be computational, analytical, or a mix of both. See the following link for descriptions of potential topics that students can explore during this project.